[CFD | ENG] Introduction to linear hyperbolic conservation laws скачать в хорошем качестве

[CFD | ENG] Introduction to linear hyperbolic conservation laws

In this video, we give an introduction to linear hyperbolic conservation laws, which are equations that commonly appear in nature, and where wave motion and convective transport are important, for instance, where a pollutant is being transported due to the movement of a fluid. We will focus on studying the simplest hyperbolic conservation law, which is the linear advection equation, where an analytical solution can be obtained. We will also discuss the discontinuous initial conditions that can be imposed in these partial differential equations (PDEs), and will explain why the finite difference methods are not suitable candidates to solve these PDE's. We will also give an introduction to characteristic curves, which is an extremely important concept that can help us to understand the behaviour of hyperbolic PDE's and can assist us in designing finite volume methods for their solution. Lastly, we discuss the boundary conditions and how we can properly impose them. This video is the first one of a two lecture series. In the next video, we will give an introduction to the finite volume methods used to solve these hyperbolic conservation laws. The next lecture can be found here:    • [CFD | ENG] Finite Volume Methods for Line...   Timestamps 00:00 Overview of the presentation 01:23 Hyperbolic PDE's. Why are they relevant? 03:37 System of hyperbolic conservation laws 08:03 Integral form of hyberbolic conservation laws 13:54 Example of hyperbolic systems 16:10 The linear advection equation 18:12 Solution of the linear advection equation 25:25 Visual representation of the solution of the PDE 27:49 Discontinuous initial solutions 31:56 Characteristic curves 38:16 Boundary conditions Links of interest Personal webpage where you can read more about my research related to fluid dynamics and other popular-science articles: https://hugocastillocom.wordpress.com